The prospects for a strong showing at the polls in Boston Tuesday when voters will decide whether to give Mayor Marty Walsh a second term "so far has not been terribly encouraging," Secretary of State William Galvin said Monday, with turnout elsewhere around the state expected to "vary widely" based on the intensity of specific races.

Galvin, whose office oversees state elections and will be providing support to local communities on Tuesday, said voters in 56 communities have local races on the ballot and 21 cities and towns will be voting in one of the three state legislative special elections on the ballot.

Local races for mayor in Lawrence, Lynn, Newton, New Bedford, Fall River, Attleboro and Framingham should help drive turnout, Galvin said, while in Boston the Brighton Democrat has lower expectations.

The lack of intensity in the race between Walsh and City Councilor Tito Jackson, along with a relatively few number of hotly contested city council races, could lead to turnout well below the 142,000 voters who cast ballots four years ago when Walsh claimed the open mayoral seat, Galvin said.

Pressed to make a prediction, Galvin said the circumstances of the current race and historical precedent lead him to believe that turnout could hover around 90,000 in Boston.

Many cities are choosing mayors, city council and school committee members and deciding local policy issues, such as where to site a high school in Lowell.

Voters in Haverhill and the 1st Berkshire district will also be electing new state representatives, and there are primaries in the race to fill Cannabis Control Commissioner Jennifer Flanagan's former state Senate seat in north central Massachusetts.

"These are really important elections at every level. Certainly at the local level, these are where the decisions that affect people where they live are made, whether it's zoning issues, public education, transportation. These are all very significant races so we hope that people will remember that and take the time to participate in these elections, because actually these are the things that will affect them the most," Galvin said.

Galvin did caution voters not to try to participate in elections in communities where they used to live, even if they only recently moved. He said this phenomenon tends to be more prevalent in local elections than statewide elections.

"That is not proper. That is not legal. They would be potentially threatening the validity of the election if they were to be decisive in their participation, so we would hope people will only vote in the communities where they actually reside, not where they once upon a time lived," Galvin said.

The chief elections officer also said that his office has received no evidence of voter fraud in Boston, despite allegations of elderly voters in Chinatown being taken advantage of through an absentee ballot scheme to influence the city council race in that district.

Galvin said his office has been in touch with the Boston elections division about making sure voters are aware of their rights, and he believes the necessary steps are being taken to ensure the integrity of the election.

While he said his focus Tuesday is on protecting the rights of voters who show up at the polls, Galvin noted a "troubled past" and competency issues in Boston with regard to handling local elections and said his office will be ready to get involved after Tuesday if evidence of fraud is presented.